[Jenne, Annalisa]

DQ channels have been created in the C1ALS model for TRX and TRY. They are called TRX_OUT and TRY_OUT and the sampling rate is 2048 Hz.

I've switches the ALS, ASC, and LSC plots on the summary pages from plotting raw frames, to plotting minute trends, instead. Now, the plots contain information, instead of being completely blank, but data is not recorded on the plots after 12UTC.

Typically, I make changes to the summary pages on my own version of the pages, found at https://ldas-jobs.ligo.caltech.edu/~eve.chase/summary/day/, where I change the summary pages for June 30 and then import such changes into the main summary pages. 

[ericQ, gautam]

Today we spent some time looking into the PDH situation at the X end. A summary of our findings.

1. There is something that I don't understand with regards to the modulation signal being sent to the laser PZT via the sum+HPF pomona box - it used to be that with 2Vpp signal from the function generator, we got ~5mVpp signal at the PZT, which with the old specs resulted in a modulation of ~0.12rad. Now, however, I found that there was a need to place a 20dB attenuator after the splitter from the function generator in order to realize a modulation depth of ~0.25 (which is what we aim for, measured by locking to the TEM00 modes of the carrier and sidebands and comparing the ratio of powers). It could be that the PZT capacitance has changed dramatically after the repair. Nevertheless, I still cant reconcile the numbers. We measured the transfer function from the LO input of the pomona box to the output with the PZT connected, and figure there should be ~70dB of attentuation (with the 20dB additional attenuator in place). But this means 1Vpp*0.0003*70rad/V = 0.02rad which is an order of magnitude away from what the ratio of powers suggest. Maybe the measurement technique was not valid. In any case, this setup appears to work, and I'm also able to send +7dBm to the mixer which is what it wants (function generator output is 3Vpp).
2. In addition to the above, I found that the demodulated error signal had a peak-to-peak of a few volts. But the PDH servo is designed to have tens of mV at the input. Hence, it was necessary to turn down the gain of the REFL PD to 10dB and add a 20dB attenuator between mixer output and servo input.
3. While Johannes and I were investigating this earlier in the afternoon, we found that the waveform going to the laser PZT was weirdly distorted (still kind of sinusoidal in shape, but more rounded, I will put up a picture shortly). This may not be the biggest problem, but perhaps there is a better way to pipe the LO signal to the PZT and mixer than what is currently done.
4. We then looked at loop transfer function and spectrum of the control signal. Plots to follow. They look okay.
5. I measured the green power coming onto the PSL table. It is ~400uW. After optimizing alignment, the green transmission is ~0.4 according to whatever old normalization we are using.
6. We then recovered the X green beatnote and looked at the ALS noise spectrum. Beatnote amplitude at the beat PD is ~ -27dBm. The coherence in the region of a few hundred Hz suggests that some improvements can be made to the PDH situation (the gain of the PDH servo is maxed out at the X end at the moment...). But the bottom line is this is probably good enough to get back to locking...

All seems very fishy. Its not good to put attenuators and filters in nilly-willy.

1. Once the post-PD bandpass has been designed and constructed, you should be able to use whatever PD gain setting gives you the best SNR. There's no need to use more PD gain than necessary; it just reduces the PD bandwidth. What is the input referred current noise of the PD at the different gain settings?
2. The open loop mixer output *should* be very large. It should be reduced to mV only when the loop is closed.
3. The better way to estimate the modulation depth is to lock the arm on red as usual and then scan the EX laser and look at the green transmission. The FSR is 3.7 MHz, so the SBs should show up well in a narrow scan around the carrier.
4. I guess its going to be tough to impedance match the splitter box to the NPRO PZT, since its impedance is all over the place at 200-300 kHz, but you could put a 50 Ohm in-line terminator in there somewhere?
5. The Bode plot seems to indicate that we could easily get a 10 kHz UGF and then switch on a Boost. Is the remote Boost switch disabled or always ON? I am suspicious of the plot and think that the coarse trace is probably missing some sharp resonances which will sneakily bite you.

After Jenne and Masayuki told that they were not able to stabilize the ALS for either arms yesterday, I looked into things with the ALS servo.

I had trouble initially trying to even stabilize the loop for a few minutes. So I measured the OLTF of the phase tracker loop and the ALS X arm servo. I changed phase tracker gain to 125 and that rendered UGF of 2KHz and phase margin of 45 degrees for the phase tracker loop.

The ALS servo gain was set such that UGF was 125Hz and phase margin 38 degrees (attached is the transfer function measurement for the servo).

I could stabilize the arm to ~500 Hz/rtHz (rms), which is twice that of what we had while we did the (PRMI+1arm ALS).

But ALS was still not stable long enough with the higher rms to even allow a cavity scan to find IR resonance. I suspect the problem to now lie with the PDH loop. We should be looking to stabilize the PDH for green if we need a stable ALS.

I'm running a test to see how stable the EX green lock is. For this purpose, I've left the slow temperature tuning servo on (there is a 100 count limiter enabled, so nothing crazy should happen).

- ALS X/Y arm stability was checked by IR locked arms.

- Basically the stability looks same as before.

Q sez: here are some ALS ASDs (in Hz/rtHz). 

The reference plots are with the arms locked on CARM/DARM with ALS. The main traces are with the arms locked on POX/POY. Alignment affects these traces a fair amount.

The X arm ALS seems no worse for the upgrade, and the PZT actuators do look pretty orthogonal when we play around with the alignment. 

While setting up for this measurement, I noticed something odd with the whitening switching for the ALS channels. For the usual LSC channels, the whitening is set up such that switching FM1 on the MEDM screen changes a BIO bit which then enables/disables the analog whitening stage. But this feature doesn't seem to be working for the ALS channels - I terminated all 4 channels at the LSC rack, and measured the spectrum of the IN1 signals with DTT in the two settings, such that I expect to see a difference in the spectra if the whitening is enabled or disabled - FM1 enabled (expected analog whitening to be engaged) and FM1 disabled (expected analog whitening to be bypassed). But I see no difference in the spectra. I confirmed that the BIO bit switching is happening at least on the software level (i.e. the bit indicator MEDM screens indicate state toggling when FM1 is ON/OFF). But I don't know if something is amiss in the signal chain, especially since we are using Hardware channels that were previously used for AS_165 and POP_55 signals.

Is the whitening shape such that we expect the terminated noise level to be below ADC Noise even when the whitening is engaged? I just checked the shape of the de-whitening filter, and it has -40dB gain above 150Hz, so the inverse shape should have +40dB gain. 

gautam 2.15pm: This was a FALSE ALARM, with the inputs terminated, the electronics noise really is that low such that it is buried under ADC noise even with +40dB gain. I cranked up the flat whitening gain from 0dB to 45dB for the X channels (but left the Y channels at 0dB). Attachment #2 is the comparison. Looks like the switching works just fine.

Summary:

I do not have an answer to the question "What is an appropriate gain for the IF amplifier stage in the D0902745 FET demod boards?", because of the following problems.

Deatils:

The plan is to lower the gain of the IF amplifier stage on the FET demodulator board from 100 to 10. As per Attachment #1, this will make the overall gain from RF beatnote from the Beat Mouth to the signal input to the D990694 whitening board +19dB, assuming "typical" values for the conversion loss of the mixer, and the various other passive components on the FET demod board. I've used numbers I measured a couple of weeks ago for the delay line loss and the cabling loss from the PSL table to the LSC rack. This in turn will set a limit on how much RF beat power we can handle, from the Beat Mouth. According to this power budget, if we have -5dBm of beat, we will have an input to the whitening board of ~6Vpp, which is about half its full range. The trouble is, I don't know what the transimpedance gain of the Fiber Beat PDs are. The datasheet suggests a "maximum gain" of 5e4 V/W, which presumably takes into account the InGaAs responsivity and the actual transimpedance gain. However, according to the last power budget I did inside the Beat Mouth, I had -8dBm of beat for a combined 400uW of PSL+EX light, which definitely does not add up. I've emailed the company to ask about the spec, haven't gotten anything useful yet...

The problem is further complicated by the fact that the fiber inside the Beat Mouth is NOT polarization maintaining, and so the actual relative polarizations of the arm IR light and the PSL IR light is unpredictable, and also uncontrolled. I suppose we could simply place a HWP before the fiber collimator at either end, and rotate the polarization until we get a desired amount of beat, but this still does not solve the problem of the polarization being uncontrolled.

I am going to characterize the demod board using E1100114. I am unsure as to the conversion loss of the mixer - the datasheet suggested a number of 8dB, but T1000044 suggests that the conversion loss is actually only 4dB. I figure it's best to just measure it. Would also be good to verify that the overall transfer function and noise of the IF amplifier stage match my expectation from the LISO model.

Option #1: Rana ordered 50ohm and 500ohm SMD resistors of the 0805 package size, I asked Steve to get a few more values just in case we want to twiddle with the gain of this stage further (specifically, I asked for values such that we can set it to x5, x3 and x1). But changing the feedback resistors modifies the overall TF shape - see e.g. Attachment #2. Need to also look at how the noise performance varies.

Another possibility is to turn down the gain of the IF amplifier stage to x10, retire the ZHL-3A, and use a lower gain amplifier in its place. We do have the recently acquired Teledyne amplifiers, but we would have to package it in such a way that it can be integrated into the existing Fiber ALS signal chain. This would allow us to handle significantly larger RF beatnote powers, which I expect we will have if we improve the mode matching into the fibers (provided the aforementioned polarization drift possibility doesn't hurt us too much).

A third possibility is to attenuate the power coupled into the fibers to lower the RF beatnote amplitude. I don't like this option so much because placing an ND filter or a PBS+HWP combo in the beam path is likely to screw up the mode-matching into the fiber collimator, which I have already spent so many hours trying to improve, but if it must be done, it must be done.

The correct option is of course the one that gives us the lowest ALS noise. It is not clear to me which one that is at this point.

Summary:

A reasonable level of RF beatnote power for operating within the specs of the demod board is 17dBm arriving at the input to the power splitter just before the delay line.

Details:

Stuff is beginning to look clearer now that I've done some initial characterization of the demod boards. I will upload a more detailed report of the characterization on the DCC page, but important findings are:

1. The overall conversion factor from RF to IF is ~2.3V IF per volt of RF.
   • 50ohm source connected to RF input of demod board, level = 10dBm on Marconi screen, consistent with inferred value from RF mon output.
   • LO driven at 14dBm by Fluke function generator.
   • The ratio was calculated for IF voltage input into a High-Z load.
   • So let's say we want to run at half the ADC full range of 10Vpp into the whitening board - this means we need to keep the RF input to <=11dBm. 
2. The Teledyne amplifier has a rated maximum input voltage of 17dBm. If we want to stay 3dB below this, we can send in 14dBm into the LO input of the demod board, which is what my characterizations were done with.

The delay line has a loss of ~3dB. The power splitter has a loss of 3dB. So putting everything together, 17dBm at the input of the power splitter gives us just the right amount of RF power to have the LO input driven at 14dBm, and the IF output be ~5Vpp into a High-Z load, which is about half the ADC full range.

After emailing the technical team at Menlo, I have uploaded the more detailed information they have given me on our wiki.

 [Manasa, Masayuki]

[revised at 10/1 pm 5:00]

As we mentioned in previous entry (elog#9171), the phase margin of ALS control was at most 20 degree. We modified the filter of C1ALS_XARM and C1ALS_YARM. The OLTF is in attachment1. Now the phase margins of both arms are more than 35 degree. I modified the FM5 filters of both servo.

FM5 filter is the filter for the phase compensation. It had the one pole at 1000 Hz and one zero at 1Hz. As you can see in attachment2, it start to lose the phase at 50 Hz. But the UGF of our ALS control loop is higher than 100 Hz, so I changed the pole from 1 kHz to 3 kHz in order to get more phase margin at UGF. The new servo have 10dB larger gain than previous filter at higer than 1kHz, but the control loop do nothing in that region, so it's no problem.

We have phase lag between 2 arms. I used same filters for both arms, so I'm wondering where these phase lag came from.

[Koji, Annalisa, Manasa]

Today we worked on the ALS servo stabilization for the Y arm.

First step: find the beat note

The beat note was found following the usual steps:

• Y arm cavity locked on IR to have a good alignment
• Y arm cavity locked on green (eventually unlocked on IR)
• beat note alignment maximized on the PSL table

Beat note amplitude = -27 dBm @ 50 MHz

PSL temperature = 31.54 degC

Laser Offset on the slow servo2 = -11011

In the GREEN HORNET we did the following changes for the Y arm:

Input Signal Conditioning

On the C1ALS-BEATY_FINE  screen the same antiwhitening filters of the C1ALS-BEATX_FINE have been reproduced. At moment, only the FM3 [10:1] is enabled.

On the C1ALS-BEATY_FINE_PHASE screen the gain was set at 3600, since the amplitude of the Q signal after the Phase rotator (BEATY_FINE_Q_ERR) was about 30. To set this value we made a proportion with respect to a previous optimized value, where the amplitude was 100 and the gain was set to 1200.

DOF filters

In order to stabilize the beat frequency, we started enabling the FM5 [1000:1] filter in the C1ALS_YARM panel, and then we started increasing the gain first in small steps (0.1), in order to understand which sign the gain should have without kicking the mirror.

We measured the Power Spectrum of the C1:ALS-BEATY_FINE_PHASE_OUT in-loop signal while varying the gain of the C1ALS_YARM servo filter.

Eventually, we enabled the following filters:

FM2 [0:1]

FM3 [1:5]

FM4 [1:50]

FM5 [1000:1]

FM6 [RG3.2]

FM7 [RG16.5]

Gain = -30.

Koji expects the UGF of the loop to be around 100-ish Hz, and he also expected the small bump around 300-400 Hz.

Then we realized that the channel we were measuring was not calibrated in unit of Hz, so we took again the measurement looking at the channel C1:ALS-BEATY_FINE_PHASE_OUT_HZ. In this case, we didn't observe any bump. Maybe the beat frequency was slightly changed from the previous measurement and the all servo shape was also different. The final value of the gain was set at -8.

The Y axis unit is missing (bad me!). It's in deg/sqrt(Hz) for the first plot and Hz/sqrt(Hz) for the second one.

I realized that I cannot open the attached plots. I'll fix them tomorrow.

The measured openloop TF of the ALS servo for each was characterized by a ZPK model.

The openloop TF can be modeled by:

1) Filter TF obtained from foton
2) Actuator response with appropriate assumption
3) Phase tracker closed loop TF
4) Delay caused by the digital control
5) anything else

For 1) ZPK models of the servo filter was obtained from foton. It turned out that the TF of FM5 doesn't match with the ZPK model in foton.
Therefore the TF was exported and fitted with LISO. This seems to be related to the pole frequency (3kHz) which is too close to Nyquist frequency (8kHz).

FM(:,1)  = zero1(f,5).*pole1(f,0.001)*5000;
FM(:,2)  = zero1(f,1).*pole1(f,0.001)*1000;
FM(:,3)  = zero2(f,4.5,1.4619).*pole1(f,0.001).*pole1(f,0.001)*20.2501*1e6;
FM(:,4)  = zero2(f,35,2).*pole2(f,3,3).*zero1(f,3000).*pole1(f,1).*pole2(f,3000,1/sqrt(2)).*pole1(f,700).*zero1(f,10).*zero1(f,350).*136e1;
FM(:,5)  = zero1(f,1).*pole1(f,4.010e3).*pole2(f,17.3211e3,1.242).*zero2(f,18.865e3,100e3);
FM(:,6)  = zero2(f,3.2,0.966775).*pole2(f,3.2,30.572);
FM(:,7)  = zero2(f,16.5,2.48494).*pole2(f,16.5,78.5807).*zero2(f,24.0,2.22483).*pole2(f,24.0,7.03551);
FM(:,8)  = 1;
FM(:,9)  = zero2(f,7.50359,1.07194).*pole2(f,1.43429,0.717146)*27.5653;
FM(:,10) = 1;
dc_gain = 14;

FM1/2/3/5/6/7/9 are used for the control.

For 2), a resonant freq of 0.97 with Q of 5 was assumed.

The model for 3) was obtained by the previous entry.

Now the measured TF was divided by the known part of the model 1) ~ 3) and empirically fitted in LISO.

### XARM ###
pole 392.5021429051 698.1992431753m
zero 42.3128869460k 31.0954443799m
pole 589.2716424428 2.8325268375
factor 8.3430140244
delay 34.7536691023p

### YARM ###
pole 416.2463334253 743.2196174175m
zero 97.9161062704M 114.6703921876m
pole 626.0463515310 2.7671041771

factor 9.0045911761
delay 34.0945727358p

These compensation TF have weird TF. Probably the frequency response of the delay and the analog AA/AI filters without the high frequency data
led the LISO make up this. I'm requesting Masayuki to provide the AA/AI data to make the estimation more reasonable.
For the servo modeling, this is sufficient and we'll go a head.

The results of the OLTF modeling are attached.

[Masayuki, Manasa]

I. ALS servo loops
After fixing things with the phase tracking loop, we checked if things were good with the ALS servo loops.
We measured the OLTF of the X and Y arm ALS servo loops. In both cases the phase margin was ~20 degrees. There was no room to set enough phase margin. So we looked at the servo filters. We tried to modify the filters so that we could bring enough phase margin, but could not get at it. So we put back the old filters as they were.

 attachment1: OLTF of the ALS XARM and YARM control loops

attachment2: Current phase budget. FM4 and FM10 are the boost filters.

II. ALS in-loop noise
Also, I found that the overall noise of the ALS servo has gone up by about two orders of magnitude (in Hz/rtHz) over the whole range of frequencies for both the arms from the last time the measurements were made. I suspect this could be from some change in the calibration factor. Did anybody touch things around that could have caused this? Or can somebody recollect any changes that I made in the past which might have affected the calibration? Anyways, I will do the calibration again.

[Annalisa, Koji, Manasa]

In order to improve the ALS stability we went ahead to check if we are limited by the sensor noise of ALS.

What we did:
RF signals similar to the beatnote were given at the RF inputs of the beatbox.
The frequency of the RF signal was set such that I_OUT was zero (zero-crossing point of the beatbox).
We measured the noise spectrum of the phase tracker output.

Measurements:
Plot 1: X ALS noise spectrum
Plot 2: Y ALS noise spectrum

Discussion:
The X arm ALS noise is not limited by the sensor noise...which means we shoudl come up with clever ideas to hunt for other noise sources.
But this does not seem to be the case for the Y arm ALS. The Y arm part of the beatbox is noisy for frequencies < 100Hz.

After looking into the details and comparing the X and Y arm parts of beatbox, it looks that amplitude of the beat signal seem to affect the Y arm ALS noise significantly and changes the noise spectrum.

To do:
Investigate the effect/limitations of amplitude of the beatnote on the X arm and Y arm beatbox.

Summary:

I came aross an interesting suggestion by Yutaro that KAGRA's low-frequency ALS noise could be limited by the fact that the IMC comes between the point where the frequencies of the PSL and AUX lasers are sensed (i.e. the ALS beat note), and the point where we want them to be equal (i.e. the input of the arm cavity). I wanted to see if the same effect could be at play in the 40m ALS system. A first estimate suggests to me that the numbers are definitely in the ballpark. If this is true, we may benefit from lower noise ALS by picking off the PSL beam for the ALS beat note after the IMC.

Details:

Even though the KAGRA phase lock scheme is different from the 40m scheme, the algebra holds. I needed an estimate of how much the arm cavity moves, I used data from a POX lock to estimate this. The estimate is probably not very accurate (since the arm cavity length is more stable than the IMC length, and the measured ALS noise, e.g. this elog, is actually better than what this calculation would have me believe), but should be the right order of magnitude. From this crude estimate, it does look like for f<10 Hz, this effect could be significant. I assumed an IMC pole of 3.8 kHz for this calculation.

I've indicated a "target" ALS performance where the ALS noise would be less than the CARM linewidth, which would hopefully make the locking much easier. Seems like realizing this target will be touch-and-go. But if we can implement length feedforward control for the arm cavities using seismometers, the low frequency motion of the optics should go down. It would be interesting to see if the ALS noise gets better at low frequencies with length feedforward engaged.

* Some updates were made to the plot:

1. Took data from Kiwamu's paper for the seismic noise
2. Overlaid measured ALS noise

What about just use high gain feedback to MC2 below 20 Hz for the IMC lock? That would reduce the excess if this theory is correct.

I have done a quickie look at Optickle to see how the linewidth of an arm cavity changes versus the configuration. 

To do this, I make different configurations, and do a sweep of ETMX.  For each configuration, I find the max peak value, and then find the points that are at half that value.  The distance between them is the full width at half max.

I get:

FWHM_DRFPMI = 3.8750e-11  meters

FWHM_PRFPMI = 3.8000e-11  meters

FWHM_SRFPMI = 2.3200e-09  meters

FWHM_FPMI =   1.1900e-09  meters

So, for the ALS to hold within 1/10th of a linewidth for the full IFO configuration, we want the ALS noise to be on the order of 3 picometers RMS.  If I recall correctly, that's about an order of magnitude better than we currently have.

                 use LOG y-scale

EDIT 8 Nov 2013, JCD:  New log-y plot:

Summary:

Between frequent MC1 excursions, I worked on ALS recovery today. Attachment #1 shows the out-of-loop ALS noise as of today evening (taken with arms locked to IR) - I have yet to check loop shapes of the ALS servos, looks like there is some tuning to be done.

On the PSL table:

• First, I locked the arms to IR, ran the dither alignment servos to maximize transmission.
• I used the IR beat PDs to make sure a beat existed, at approximately.
• Then I used a scope to monitor the green beat, and tweaked steering mirror alignment until the beat amplitude was maximized. I was able to improve the X arm beat amplitude, which Koji and Naomi had tweaked last week, by ~factor of 2, and Y arm by ~factor of 10.
• I used the DC outputs of the BBPDs to center the beam onto the PD.
• Currently, the beat notes have amplitudes of ~-40dBm on the scopes in the control room (there are various couplers/amplifiers in the path so I am not sure what beatnote amplitude this translates to at the BBPD output). I have yet to do a thorough power budget, but I have in my mind that they used to be ~-30dBm. To be investigated.
• Removed the fiber beat PD 1U chassis unit from the PSL table for further work. The fibers have been capped and remain on the PSL table. Cleaned the NW corner of the PSL table up a bit.

To do:

• Optimization of the input pointing of the green beam for X (with PZTs) and Y (manual) arms.
• ALS PDH servo loop measurement. Attachment #1 suggests some loop gain adjustment is required for both arms (although the hump centered around ~70Hz seem to be coming from the IR lock).
• Power budgeting on the PSL table to compare to previous such efforts.

Note: Some of the ALS scripts are suffering from the recent inablilty of cdsutils to pull up testpoints (e.g. the script that is used to set the UGFs of the phase tracker servo). The workaround is to use DTT to open the test points first (just grab 0.1s time series for all channels of interest). Then the cdsutils scripts can read the required channels (but you have to keep the DTT open).

• Aligned IFO to IR.
  • Ran dither alignment to maximize arm transmission.
  • Centered Oplev reflections onto their respective QPDs for ITMs, ETMs and BS, as DC alignment reference. Also updated all the DC alignment save/restore files with current alignment. 
• Undid the first 5 bullets of elog13325. The AUX laser power monitor PD remains to be re-installed and re-integrated with the DAQ.
  • I stupidly did not refer to my previous elog of the changes made to the X end table, and so spent ages trying to convince Johannes that the X end green alignment had shifted, and turned out that the green locking wasn't going because of the 50ohm terminator added to the X end NPRO PZT input. I am sorry for the hours wasted 
  • GTRY and GTRX at levels I am used to seeing (i.e. ~0.25 and ~0.5) now. I tweaked input pointing of green and also movable MM lenses at both ends to try and maximize this. 
  • Input green power into X arm after re-adjusting previously rotated HWP to ~100 degrees on the dial is ~2.2mW. Seems consistent with what I reported here.
  • Adjusted both GTR cameras on the PSL table to have the spots roughly centered on the monitors.
  • Will update shortly with measured OLTFs for both end PDH loops.
  • X end PDH seems to have UGF ~9kHz, Y end has ~4.5kHz. Phase margin ~60 degrees in both cases. Data + plotting code attached. During the measurement, GTRY ~0.22, GTRX~0.45.

Next, I will work on commissioning the BEAT MOUTH for ALS beat generation. 

Note: In the ~40mins that I've been typing out these elogs, the IR lock has been stable for both the X and Y arms. But the X green has dropped lock twice, and the Y green has been fluctuating rather more, but has mangaged to stay locked. I think the low frequency Y-arm GTRY fluctuations are correlated with the arm cavity alignment drifting around. But the frequent X arm green lock dropouts - not sure what's up with that. Need to look at IR arm control signals and ALS signals at lock drop times to see if there is some info there.

I worked on recovering ALS today. Alignments had drifted sufficiently that I had to to the alignment on the PSL table onto the green beat PDs for both arms. As things stand, both green (and IR) beats have been acquired, and the noise performance looks satisfactory (see Attachment #1), except that the X beat noise above 100Hz looks slightly high. I measured the OLTF of the X end green PDH loop (after having maximized the arm transmission, dither alignment etc, measurement done at error point with an excitation amplitude of 25mV), and adjusted the gain such that the UGF is ~10kHz (see Attachment #2).

I've been working on getting a working ALS up and running. Things are in a bit of a transient state right now; I'm off to softball and dinner, and will resume work tonight. There will be a more detailed ELOG then, but here are some quick notes:

• c1als has been gutted, phase trackers are working successfully in c1lsc frontend. All channel names remain the same. 
• BEATX is on the ADC channels where AS165 used to live, BEATY at POP55. 
• Used a marconi to drive the aLIGO LSC demod board in the LSC rack, was able to lock digital phase tracker on two channels
• Noise looks pretty cruddy. Lots of 60Hz harmonics on both channels, maybe from marconi drive? Pickup in the delay line?
• BEATX whitening filter maybe has something fishy going on; excess noise at 2kHz
• Unclear if BEATY whitening filter is actually doing anything. 
• Whitening gain switching works fine for both, though. Haven't revisited the switching code, so its controlled in the old RFPD place for now.
• Whitening triggering is not set up, will require some thought and model work that isn't neccesary yet. 
• Agilent analyzer, marconi, and old delay lines are currently stashed behind the LSC rack; I will resume work with them tonight. 

The main thing left to do is to install the RF amplifiers at the PSL table and route the green beat signals over to the LSC rack. I fear that some investigation into the whitening filters will be neccesary to make the performance adequate, however. 

Too sleepy to make full ELOG. Stay tuned. 

Two 25dB amplifiers (with fins!) are living in the top shelf on the PSL table, inputs currently grounded. I broke out the fused 24V power from the AOM driver to power the two amps and the AOM driver. I used the POP55 and AS165 heliax cables to get their outputs to the LSC rack, through delay lines, into demod board. 

Driving with -20dBm at 55MHz, the BEATX signal chain has about 60Hz RMS noise, which is about what I measured for driving the old beatbox with a marconi. High frequency noise is a much nicer shape, though. The BEATY signal didn't seem to be getting through, will double check soon. 

Still old delay cables, not nicely shielded or isolated or anything. We'll have to pipe the monitor signal from the LSC rack over to the control room analyzer now. 

Turns out the reason that the BEATY signal wasn't working is that one of the two RF amplifiers (both of which are model ZHL-32A), isn't amplifying. Voltage at the pins is fine, so maybe its just broken. When the ZHL-3As that Rana ordered arrive, I'll install those. 

Switching the working amplifier between the two channels, and using a Marconi driving -20dBm (the Y green beatnote amplitude), the phase tracker output RMSs are 70Hz and 150Hz for X and Y, respectively, which isn't too exciting. There is enough whitening gain and filtering that I don't think ADC noise is an issue (The magnitude of the phase tracker Q is ~10kcounts after +6dB whitening gain). 

The RMS in both channels mostly comes from a whole mess of 60Hz harmonics. I'll see what I can do by taking better care of the delay line cables, but it is kind of weird that this would be worse now, given that there was little care given to them before either.

Also, for now, so I don't have to lug the marconi around everywhere, I'm currently driving both channels of the demod board with a spare 55MHz LO output of the LSC LO distribution box, which ends up being a factor of 5 smaller phase tracker error signal, but the noise level is about the same as with the marconi. 

In calculating the above numbers, I assumed a DC transimpedance of 10 khhms and an RF Transimpedance of ~800 V/A.

[Elog14480]: per these calculations, with the NewFocus 1611 PDs, we cannot achieve shot noise limited sensing for any power below the rated maximum for linear operation (i.e. 1mW). Moreover, the noise figure of the RF amplifier we use to amplify the sensed beat note before driving the delay-line frequency discriminator is unlikely to be the limiting noise source in the current configuration. Rana suggested that we get two Gain Blocks. These can handle input powers up to ~10dBm while still giving us plenty of power to drive the delay line. This way, we can (i) not compromise on the sacred optical gain, (ii) be well below the 1dB compression point (i.e. avoid nonlinear noise effects) and (iii) achieve a better frequency discriminant. 

Temporary fix: While the gain blocks arrive, I inserted a 10dB (3dB) attenuator between the PSL+EX (PSL+EY) photodiode RF output and the ZHL-3A amplifiers. This way, we are well below the 1dB compression point of said RF amplifiers, and also below the 1dB compression point of the on-board Teledyne AP1053 amplifiers on the demodulator boards we use.

Nest steps: Rana is getting in touch with Rich Abbott to find out if there is any data available on the noise performance of the post-mixer IF amplifier stage in the 0.1 -30 Hz range, where the voltage and current noise of the AD829 OpAmps could be limiting the DFD performance. But in the meantime, the ALS noise seems good again, and there is no evidence of the sort of CARM/DARM coupling that motivated this investigation in the first place. Managed to execute several IR-->ALS transitions tonight in the PRFPMI locking efforts (next elog).

No new Teledyne AP1053s were harmed in this process - I'll send the 5 units back to Rich tomorrow.

To get a better look at how to do fast ALS, I took some "Plant TF" measurements of the X arm. 

Specifically, in single arm POX lock and the both Y TMs misaligned, I used the SR785 to inject into EXC B of the common mode board with the CM fast output gain and IMC IN2 gain both at 0dB, and looked at the transfer function of that excitation into the analog ALSX I and AS55 Q out-of-loop signals. (ALSX I tuned to a zero crossing via the delay line box as usual.)

My expectation was to see them only differ by the IR single arm cavity pole, which should be around 8-9kHz ( FSR/450 = 3.9MHz/450 ~ 8.6kHz). The green cavity pole at ~18k shouldn't show up since we're not touching the green light, and the IMC pole at ~3.8kHz shouldn't show up since this is well within the IMC loop bandwidth and we're actuating on its error point.  

Instead, I see them differ by a double pole at 4.3kHz. (or zero, if you look at it the reciprocal way). Vectfit actually fits them as a slightly complex pair, with a Q of 0.53/ I imagine that the wiggles are due to the digital control loop.

My question is: why is there a double zero here? Where has my reasoning led me astray?

ALS is the comparison of the PSL laser freq vs the end laser freq that is locked to the arm cavity resonant freq

On the other hand, the AS55 PDH is the comparison of the PSL laser freq after the IMC vs the arm cavity resonant freq. Here the PDH signal involves the arm cavity pole.

In total you observe the difference by the IMC cav pole + the arm cav pole.

Ah, I understand it now! Since the additive offset path keeps the post-cavity frequency TF flat, the pre-cavity frequency must grow above the cavity pole, which is why ALS sees a zero. 

Ok, so this means we want to apply two lowpasses to the ALS signal for use as fast CARM control, if we want it to be capable of scalar blending with REFL11: one at ~120Hz to imitate the CARM coupled cavity pole present in REFL11, and one at ~3.8kHz to undo the "IMC cavity zero" present in ALS. 

At this point, I'm starting to prefer an active circuit to do this lowpassing; using LISO to check designs for two cascaded passive LPFs it looks like the ALS signal would have to be attenuated by a factor of ~20 at DC if we don't use resistors smaller than 1k, given the low input impedence of the CM board. 

I worked a little bit on the Y arm ALS today. 

• Started by locking the Y arm to IR with POY, and then ran the dither alignment script to maximize Y arm transmission.
• Green TRY DC monitor was around 0.16, whereas I have seen ~0.45 when we were doing DRFPMI locking.
• So I went to the Y end table and tweaked the steering mirrors a little. I was able to get GTRY to ~0.42. I think this can be tweaked a little further but I decided to push on for tonight.
• The beat amplitude on the network analyzer in the control room is comparable to the X arm beat now.
• Adjusted the gain of the phase tracker servos, cleared phase history.
• Looking at the ALS beat noise with the arms locked to IR and the slow ALS temperature control loops ON (see Attachment #1), the current measurements line up quite well with the reference traces.

I am now going to measure the OLTFs of both green PDH loops to check that the overall loop gain is okay, and also check the measurement against EricQ's LISO model of the (modified) AUX green PDH servos. Results to follow.

Some weeks ago, I had moved some of the Green steering optics on the PSL table around, in order to flip some mirror mounts and try and get angles of incidence closer to ~45deg on some of the steering mirrors. As a result of this work, I can see some light on the GTRY CCD when the X green shutter is open. It is unclear if there is also some scattered light on the RFPDs. I will post pictures + a more detailed investigation of the situation on the PSL table later, there are multiple stray green beams on the PSL table which should probably be dumped.

As I was writing this elog, I saw the X green lock drop abruptly. During this time, the X arm stayed locked to the IR, and the Y arm beat on the control room network analyzer did not jump (at least not by an amount visible to the eye). Toggling the X end shutter a few times, the green TEM00 lock was re-acquired, but the beatnote has moved on the control room analyzer by ~40MHz. On Friday evening however, the X green lock held for >1 hour. Need to keep an eye on this.

We found the PDH servo gain for Y arm green was set at 2 (too low). The gain was set to 8.6 (based on earlier OLTF measurement elog 8817).

The ALS out-of loop noise was remeasured. We also measured the out-of loop noise of each arm while the other arm had no green (shutter closed). There doesn't seem to be any difference in the noise (between green and orange for Y arm and red and pink for the X arm) except that the noise in the X arm was slightly low for the same conditions (blue and red)  when measurement was repeated.

TRANSLATION by Jenne:  We first locked both X and Y for IR using the LSC, and X and Y for green using the analog PDH servos.  We measured the _PHASE_OUT_Hz calibrated error signals for both X and Y in this configuration - this gives us the out of loop noise for the ALS system, the Green and Blue traces in the plot.  We then closed the X end shutter, and measured the Y arm's error signal (to check to see if there is any noise contribution from the suspected X-Y cross beatnote).  Then, we closed the Y end shutter, relocked the Xarm on green's 00 mode, and measured the X arm's error signal.  We weren't sure why the Pink curve was smaller than the Blue curve below a few Hz, so we repeated the original measurement with both arms dichroic.  We then got the Red curve.  So, we should ignore the blue curve (although I still wonder why the noise changed in such a short time period - I don't think we did anything other than unlock and relock the cavity), and just see that the Green and Gold curves look similar to one another, and the Red and Pink curves look similar to one another.  This tells us that at least the out of loop noise is not affected by any X-Y cross beatnote.

I have taken out of loop spectra for both arms, by looking at POX/POY while the arms were controlled with ALS.

To do this, I put the POY11 Q signal directly to the whitening board, which meant that I removed the cable coming from the common mode board.  (Now that we're doing CM stuff again, I have put it back, so POY is still in the slightly weird "going through the CM slow path" situation). 

For the locking, both arms had FMs 1, 2, 3, 5, 6 engaged.  Yarm had a gain of +17, Xarm had a gain of -17. 

Y beatnote was 98.6MHz with a peak height of -22 dBm.  X beatnote was 45.0MHz with a peak height -11 dBm.

I drove ITMY at 503.1 Hz with 100 counts.  I drove ITMX at 521.1 Hz with 25 cnt. 

Koji helped me match up the peak heights between the FINE_PHASE_OUT_HZ calibrated signals and the PDH signals. 

The out of loop noise is definitely below 1kHz rms now, which is better than it was!  Hooray!

Beat notes were recovered for both the arms.

I locked the arms to IR using PDH and measured the ALS out of loop noise at the phase tracker output.

The Y arm has the same 300Hz/rtHz rms. The X arm rms noise measures nearly the same as the Y arm in the 5-500Hz region (X arm has improved nearly 10 times after the last whitening filter stage change  old elog ).

The noise in the ALSX error signals could be related to the bad alignment and conditions at the X end.

 I have modified the script ALSchangeOffsets.py (in ..../scripts/ALS/) to also handle a "CARM" situation.  There is a new button for this on the ALS in LSC screen.  This script takes the desired offset, and puts half in the ALSX offset, and half in the ALSY offset.  Whatever offset you ask for is given the sign of the input matrix element in the ALS->CARM row of the input matrix.  For example, if you ask for a CARM offset of 1, and the matrix elements are ALSX->CARM=+1 and ALSY->CARM=-1 (because your beatnotes are on opposite sides of the PSL), you will get an offset of +0.5 in ALSX and -0.5 in ALSY, which should be a pure CARM offset. The offsets get set as expected, but I haven't had a chance to test it live while the arms are locked. 

I also want to write a script that will average the IN1 of the 1/sqrt(TR) signals, and put that number into the 1/sqrt(TR) offsets.  If this is run when we are at about half fringe, this will set the zero point of the 1/sqrt(TR) signals to the half fringe (or where ever we are).  Then, we need a script similar to the ALS CARM one, to put offsets into the CARM combination of 1/sqrt(TR)s. 

I think that putting the offsets in before the servo filters will mean that the signals coming out of the input matrices will already be at their zero points, so we won't have as much trouble shifting from ALS to IR.

Koji mentioned to me (and elogged) that he was unsuccessful locking the ALS using the LSC servos.  He suggested I look into this.

So, rather than just looking at the transfer function between POX or POY and the green beatnotes at a single frequency, I did a whole transfer function.  The point was to see if the TF is flat, and if we get any significant phase lag in the transfer from c1als to c1lsc.  (c1als is running on the IOO machine, so an RFM connection is involved in getting it over to the LSC machine.)

In the first figure, I have plotted POX vs. Beatnote_PHASE_OUT (ALS error signal, still in the c1als model), and POX vs. ALSX_IN1 (the ALS error signal, after transfer over to the c1lsc model).  You can see that we have a little phase lead in the blue transfer function, and fairly significant phase lag in the red (red is after transfer over to the lsc model).  In the grand scheme of things, the magnitude is fairly flat, however that is not perfectly true - the peaks seen near 50 Hz and 300Hz are repeatable.  The relative phase lag between the "BEATX" version of the signal in the ALS model, and the "ALSX" version of the signal in the LSC model is 15 degrees at 200 Hz, which corresponds to 33 usec.   

The second figure is the same as the first, except for the Yarm.  The relative phase lag between the ALS version of the error signal and the LSC version is 16 degrees at 200 Hz, which is about 35 usec.

As a side note, before trying any ALS locking, I took a spectrum of the beatnote (in the ALS model) while the arms were locked with IR:

To check things, I made sure that I could lock the Xarm ALS using the old ALS system - I was able to do so.  (Has someone put the "watch" script as a constantly-on thing?  It's kind of nice not to have to turn it on, although we'll need to change it to turn off the LSC versions of the servos eventually). 

Then, I tried locking the Xarm using the LSC system (using only FM5 of the regular LSC-XARM filter bank).  Like Koji, I was not able to acquire lock.  As a next step, I copied all of the LSC-XARM filters into an empty filter module, LSC-XXXDC (the first one on the list underneath LSC-XARM), and copied over the ALS Xarm filters to the LSC Xarm filter bank.  I then tried to acquire lock, but am unable to get it to stay.  Using the ALS system, when you put in a small gain, the beatnote starts to settle down, and as you increase the gain, the beatnote stops moving (as seen on the spectrum analyzer) almost completely.  However, using the LSC system, the beatnote never really stops moving or settles down.  And if I increase the gain, I push the ETM hard enough that I lose green lock.  I have put the regular LSC filters back for now.

Here is a plot from Foton comparing the FM5 filter modules from the LSC-XARM (regular IR locking) and the ALS-XARM servo.  They are pretty different, and have 10 degrees of phase difference at 200 Hz, because 2 of the 3 poles are complex in the LSC version, while the ALS version is just a single real pole.

Anyhow, I am declaring it to be dinnertime, and I plan to return in a few hours. Since I put the regular LSC filters back (since I'm going to have to realign after dinner anyway), the IFO should be in its nominal state if anyone wants to come in and play with it.

Hmm. Wierd. Can you look at the TFs between ETMX-EXC and the error signals so that we can identify which one has these structures.

It looks like its somehow a discrepancy between the TFs of each error signal, because features are similar, and present, in both error signals.

Last night, as well as tonight, the ALS seems not quite as robust as it was earlier in the week.

I have just taken noise spectra, and ALS is definitely more noisy than usual. 

These plots are with the arms held in CARM and DARM mode, with servo gains of 8. I was seeing the beginnings of gain peaking at a gain of 10, so I turned it back to 8.  Our ALS in-loop RMS is usually something like a few hundred Hz, but I'm seeing over 1kHz, so I have a factor of 4 or 5 too much noise.  Why?!?!?

I re-checked the ALS noise in the following configurations:

• PRM is misaligned.
• Michelson is not locked.
• TRX/TRY is maintained at ~1.

1. Arm lengths are controlled using POX/POY as a sensor, and the ETMs as actuators [orange traces in Attachment #1].
   • EX laser frequency is locked to the arm cavity length using the end PDH servo.
   • ALS beat note frequency fluctuations are read out using the calibrated DFD channels.
   • In this config, the DFD outputs are the out-of-loop sensor.
2. Arm lengths are controlled using the ALS beat frequencies as a sensors [blue traces in Attachment #1]
   • The control is no longer in the XARM/YARM basis, but in the CARM/DARM basis.
   • The CARM actuator is MC2, the DARM actuator is an admixture of the ETMs (equal magnitude of output matrix element, opposite sign).
   • The calibrated POX/POY photodiodes are used as the out-of-loop sensor in this config.

The RMS noise sensed by POX/POY is ~20pm, which is somewhat higher than the best I've seen (maybe the arms are moving more at the time of measurement or the AUX PDH loops need a bit of touching up). But the orange traces in the top row of Attachment #1 are already ~x2 better than the equivalent traces from when we were using the green beams to make the beats. So it's hard to explain the 0-300 fluctuations in the arm powers when the CARM offset is reduced to 0 - i.e. the ALS noise is becoming worse as I reduce the CARM offset (= have more circulating power compared to the conditions of this test). I assume the transmission is Lorentzian, in which case even if we have 5x the CARM linewidth worth of ALS noise, we should see the arm power fluctuate between ~10 and 300. 

* I notice that a big jump in the RMS sensed by POX/POY comes from the 24 Hz peak, which is presumably the Roll mode coupling to length - maybe a ResG can make the situation better. The high frequency noise can also be probably rolled off better.

[Yuta, Hiroki]

*This work was done on Aug. 10th.

We measured the ALSX noise and ALSY noise on Aug. 10th as shown in Attachment 1.
We used a digagui template to measure the noise and it had the reference of the previous measurement (but the date was not shown).
The measured ALSX this time (red) was noisier compared to the previous result (magenta) in almost all the frequency range.
The measured ALSY (blue) was noisier than the previous result (cyan) above ~ 50 Hz with the flat shape but was better below ~ 10 Hz for some reason.

There was some UNELOGGED work at EX today. The DFD outputs were also hijacked for loss measurement. Unclear who the culprit was, but there is now a broad noise bump centered around ~180 Hz in the ALS X noise curve, which certainly wasn't there yesterday. Maybe let's keep the few working systems working, it is annoying to have to deal with these auxiliary issues every night. I'll push ahead with locking, hopefully the ALS noise is "good enough".

AUX PDH Loop update

I used D1400293 to get the latest logged details about the universal PDH box used to lock the green laser at X end. The uPDH_X_boost.fil file present there was used to obtain the control model for this box. See attachment one for the code used. Since there is a variable gain stage in the box, I tuned the gain of the filter model F_AUX in ALS_controls.yml to get the maximum phase margin in the PDH lock of the green laser. Unity gain frequency of 8.3 kHz can be achieved in this loop and as Gautam pointed out earlier, it can't be increased much further without changes in the box.

ALS Noise Budget update

The ALS control model remains stable with a reduction in total estimate noise because of the above update. There are few things to change though:

• This model is for a single arm locking where the beatnote signal between green laser and frequency doubled main laser is fed back to ETM at X end. Currently, Gautam is using a different scheme to lock where the feedback is sent to PSL-MC loop and the beat is taken between IR signals.
• In the LSC controls, I couldn't find a place where the digital ALS filter I have been optimizing and Kiwamu used, was placed. From what I gathered, after demodulation of beat note signal, a digital PLL is employed and the error signal is few to the Servo Filters directly. I might be missing some script which specifically switches on a particular set of filter modules in the XARM/YARM path when arms are locked through ALS.
• Another straight forward job for me is to verify the PSL-MC loop parameters with he TTFSS used. I'll do this next.

For all the loops where we drive the NPRO PZT, there is some notch/resonance feature due to the PZT mechanical resonance. In the IMC loop this limits the PZT/EOM crossove to be less than 25 kHz. I don't have a model for this, btu it should be included.

If you hunt through the elogs, people have measured the TF of ALS NPRO PZT to phase/frequency. Probably there's also a measured ALS PDH loop somewhere that you could use to verify your model.

The only two PZT Phase modulation transfer function measurements I could find are 40m/15206 and 40m/12077. Both these measurements were made to find a good modulation frequency and do not go below 50 kHz. So I don't think these will help us. We'll have to do a frequency transfer function measurement at lower frequencies.
I'm still looking for ALS PDH loop measurements to verify the model. I found this 40m/15059 but it is only near the UGF. The UGF measured here though looks very similar to the model prediction. A bit older measurement in 2017 was this 40m/13238 where I assume by ALS OLTF gautum meant the green laser PDH OLTF. It had similar UGF but the model I have has more phase lag, probably because of a 31.5 kHz pole which comes at U7 through the input low pass coupling through R28, C20 and R29 (See D1400293)

If the green laser is not being used, can I go and take some of these measurements myself?

Koji recommended that I can add whitening filters to suppress ADC noise easily. I added a filter before ADC in ALS loop with 4 zeros at 1.5 Hz and 4 poles at 100 Hz and added a reversed filter in the digital filter of ALS. This did not change the performance of the loop but significantly reduced the contribution of ADC noise above 1 Hz. One can see ALS_controls.yaml for the filter description. Please let me know if this does not make sense or there is something that I have overlooked.

Now, the dominant noise source is DFD noise below 100 Hz and green laser frequency noise above that. For DFD noise, I used data dating back to Kiwamu's paper. The noise contribution from DFD in the model is lower than the latest measured ALS noise budget post on elog. I'll look further into design details and noise of DFD.

Code, data, and schematics

Setting the record straight

I found out an error I did in copying some control model values from Kiwamu's matlab code. On fixing those, we get a considerably reduced amount of total noise. However, there was still an unstable region around the unity gain frequency because of a very small phase margin. Attachment 3 shows the noise budget, ALS open-loop transfer function, and AUX PDH open-loop transfer function with ALS disengaged. Attachment 4 is the yaml file containing all required zpk values for the control model used. Note that the noise budget shows out-of-loop residual arm length fluctuations with respect to PSL frequency. The RMS curve on this plot is integrated for the shown frequency region.

Trying to fix the unstable region

Adding two more poles at 100 Hz in the ALS digital filter seems to work in making the ALS loop stable everywhere and additionally provides a steeper roll-off after 100 Hz. Attachment 1 shows the noise budget, ALS open-loop transfer function, and AUX PDH open-loop transfer function with ALS disengaged. Attachment 2 is the yaml file containing all required zpk values for the control model used. Note that the noise budget shows out-of-loop residual arm length fluctuations with respect to PSL frequency. The RMS curve on this plot is integrated for the shown frequency region.

But is it really more stable?

• I tried to think about it from different aspects. One thing is sure that  remains greater than 1 in all of the frequency region plotted for. This is also evident in the common-mode to residual noise transfer function which shows no oscillation peaks and is a clean mirror image of the open-loop transfer function (See Attachment 1, page 2).
• Another way is to look for the phase margin. This is a little controversial way of checking stability. For clarity, the open-loop transfer function I'm plotting does not contain the '-1' feedback in it. So the bad phase value at unity gain frequency is -180 degrees (or 180 degrees) for us. I've taken the difference from the closest side and got 76.2 degrees of phase margin.
• Another way I checked was by plotting a Nyquist plot for the open-loop transfer function. It is said that if the contour does not encircle the point '-1' in the real axis, then the loop would be stable even if the where is the frequency where phase lag becomes -180 degrees at the lowest frequency. For us, is at 1 Hz because of the test mass actuator pole. But I have verified that the Nyquist contour of the open-loop transfer function does not encircle '-1' point. I have not uploaded the Nyquist plot as it is not straight forward to plot. Because of large dc gain, it covers a large region and one needs to zoom in and out to properly follow what the contour is really doing. I didn't get time to make insets for it.

Is this close to reality?

For that, we'll have to take present noise source estimates but Gautum vaguely confirmed that this looked more realistic now 'shape-wise'. If I remember correctly, he mentioned that we currently can achieve 8 pm of residual rms motion in the arm cavity with respect to the PSL frequency. So we might be overestimating our loop's capability or underestimating some noise source. More feedback on this welcome and required.

Additional Info:

The code used to calculate the transfer functions and plot them is in the repo 40m/ALS/noiseBudget

Attachment 5 here shows a block diagram for the control loop model used. Output port 'Res_Disp' is used for referring all the noise sources at the residual arm length fluctuation in the noise budget. The open-loop transfer function for ALS is calculated by -(ALS_DAC->ALS_Out1 / ALS_DAC->ALS_Out2) (removing the -1 negative feedback by putting in the negative sign.) While the AUX PDH open-loop transfer function is calculated by python controls package with simple series cascading of all the loop elements.

I think the digital loop in the ALS budget is too optimistic. You have to include all the digital delays and anti-aliasing filters to get the real response.

aslo, I recommend grabbing some of the actual spectra from the in-lock times with nds and using the calibrated spectra as inputs to this mode. Although we don't have good models of the stack, you can sort of infer it by using the calibrated seismometer data and the calibrated MC_F or MC_L channels (for IMC) or XARM/YARM signals for those.

This is not a reply to comments given to the last post; Still working on incorporating those suggestions.

Trying out a better filter from scratch

Rana suggested looking first at what needs to be suppressed and then create a filter suited for the noise from scratch. So I discarded all earlier poles and zeros and just kept the resonant gains in the digital filter. With that, I found that all we need is three poles at 1 Hz and a gain of 8.1e5 gives the lowest RMS noise value I could get.

Now there can be some practical reasons unknown to me because of which this filter is not possible, but I just wanted to put it here as I'll add the actual noise spectra into this model now.

Few questions:

• What anti-aliasing filters are used in ALS?
• Is the digital delay fixed to a constant upper limit or is it left to change as per filters? I have already used a 470 us delay (modeled with Pade 4th order approximation).
• I could not find a good place where channel names are listed with corresponding meaning. Where can I find them?
• Is there a channel which keeps a record of lock status? In short, how do I find the in-lock times

This ALS loop is not stable. Its one of those traps that comes from using only the Bode plot to estimate the loop stability. You have to also look at the time domain response - you can look at my feedback lecture for the SURF students for some functions.